Hi,
I wonder if anyone could either agree or disagree with what I find: that for the ground state of a one-dimensional isotropic ferromagnetic spin-1/2 chain of length 4 the sum of the diagonal 0.24999999999999997 and off-diagonal 0.55359228338317501 onsite spin correlations do not sum close to 0.75, when they are computed using sparsediag without imposing conservation of ‘Sz’?
As it stands, I cannot proceed to interpret my ALPS results.
With best regards, Eoin
On 12 Aug 2014, at 11:37, Eoin Quinn epquinn@pks.mpg.de wrote:
Dear ALPS users,
I have a question regarding the calculation of correlations with sparsediag.
Let me take for an example a one-dimensional ferromagnetic spin chain of length 4. I will not impose ‘Sz’ conservation as the problem I am having arises when ‘Sz’ is not conserved, once I impose it all works well. The following are my input parameters for the calculation:
<PARAMETERS> <PARAMETER name="MEASURE_CORRELATIONS[Offdiagonal spin correlations]">Splus:Sminus</PARAMETER> <PARAMETER name="NUMBER_EIGENVALUES">1</PARAMETER> <PARAMETER name="BC">periodic</PARAMETER> <PARAMETER name="local_S">0.5</PARAMETER> <PARAMETER name="J">-1</PARAMETER> <PARAMETER name="L">4</PARAMETER> <PARAMETER name="LATTICE">chain lattice</PARAMETER> <PARAMETER name="SEED">911696590</PARAMETER> <PARAMETER name="W">1</PARAMETER> <PARAMETER name="MODEL">spin</PARAMETER> <PARAMETER name="MODEL_LIBRARY">aux/models.xml</PARAMETER> <PARAMETER name="LATTICE_LIBRARY">aux/lattices.xml</PARAMETER> <PARAMETER name="MEASURE_CORRELATIONS[Diagonal spin correlations]">Sz</PARAMETER> <PARAMETER name="CONSERVED_QUANTUMNUMBERS"></PARAMETER> <PARAMETER name="TOTAL_MOMENTUM">4.712388980384689674</PARAMETER> </PARAMETERS>
The output for the ground state is then
<EIGENSTATES number="1"> <QUANTUMNUMBER name="TOTAL_MOMENTUM" value="0"/> <EIGENSTATE number="0"> <SCALAR_AVERAGE name="Energy"><MEAN>-1</MEAN></SCALAR_AVERAGE> <VECTOR_AVERAGE name="Diagonal spin correlations"> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 0 )"><MEAN>0.24999999999999997</MEAN></SCALAR_AVERAGE> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 1 )"><MEAN>0.0078869096162297037</MEAN></SCALAR_AVERAGE> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 2 )"><MEAN>0.0078869096162296551</MEAN></SCALAR_AVERAGE> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 3 )"><MEAN>0.0078869096162297071</MEAN></SCALAR_AVERAGE> </VECTOR_AVERAGE> <VECTOR_AVERAGE name="Offdiagonal spin correlations"> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 0 )"><MEAN>0.55359228338317501</MEAN></SCALAR_AVERAGE> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 1 )"><MEAN>0.24211309038377027</MEAN></SCALAR_AVERAGE> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 2 )"><MEAN>0.2421130903837703</MEAN></SCALAR_AVERAGE> <SCALAR_AVERAGE indexvalue="( 0 ) -- ( 3 )"><MEAN>0.24211309038377027</MEAN></SCALAR_AVERAGE> </VECTOR_AVERAGE> </EIGENSTATE> </EIGENSTATES>
The problem I am having is that the diagonal and off diagonal components of the ( 0 ) -- ( 0 ) spin correlations do not sum to 3/4 = S(S+1) = \vec{S}.\vec{S}, whereas I would expect them to.
Do I understand correctly that the "Diagonal spin correlations" give <S^z(i) S^z(j)> and the "Offdiagonal spin correlations" give <S^x(i) S^x(j) + S^y(i) S^y(j)>?
With best regards, Eoin